You have to give them your phone number to sign up.

That phone number is tied to a real person by government records. Sure if you're in say Russia it makes it a lot harder for the FBI to identify you because Russian phone companies won't necessarily respect a US legal request. But if you're anywhere within the west (US, Canada, EU, Australia, NZ) they can ID you unless you go to the trouble of getting an anonymous phone number that works with the SMS verification services they use and maintaining that number for when they lock your account and demand to verify you again all while accessing it over a VPN. That plus no encryption by default makes it not very secure at all.

But fundamentally you could do the same thing securely with any service, you could do that with Facebook, with Twitter, and the list goes on if you can get good reliable anonymous phone numbers. Telegram isn't special in that way.